The Stability Analysis of the Adaptive Fading Extended Kalman Filter

The well-known conventional Kalman filter gives the optimal solution but requires an accurate system model and exact stochastic information. Thus, the Kalman filter with incomplete information may be degraded or even diverged. In a number of practical situations, the system model and the stochastic information are incomplete. To solve this problem, a new adaptive fading Kalman filter (AFKF) using the forgetting factor has recently been proposed. This paper extends the AFKF to nonlinear system models to obtain an adaptive fading extended Kalman filter (AFEKF). The forgetting factor is generated from the ratio between the calculated innovation covariance and the estimated innovation covariance. Based on the analysis result of Reif for the EKF, the stability of the AFEKF is also analyzed.